2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127646We prove that all finite W-algebras associated with nilpotent elements e in a complex semisimple Lie algebra g have finite-dimensional representations. In order to obtain this result we establish a connection between primitive ideals of U(g) attached to the nilpotent orbit containing e and finite-dimensional representations of the reduced enveloping algebra assiciated with e over an algebraically closed field of finite characteristic.19 pages, minor corrections and up-dates, the new version is accepted for publicationRepresentation TheoryQuantum Algebra17B35; 17B63; 17B81text